TRIANGLE CENTERS

Long before the first pencil and paper, some curious person drew a triangle in the sand and bisected the three angles. He noted that the bisectors met in a single point and decided to repeat the experiment on an extremely obtuse triangle. Again, the bisectors concurred. Astonished, the person drew yet a third triangle, and the same thing happened yet again!

Unlike squares and circles, triangles have many centers. The ancient Greeks found four: incenter, centroid, circumcenter, and orthocenter. A fifth center, found much later, is the Fermat point. Thereafter, points now called nine-point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added to the literature. In the 1980s, it was noticed that these special points share some general properties that now form the basis for a formal definition of triangle center

The Encyclopedia of Triangle Centers lists many centers, but without pictures. The purpose of this page is to introduce a collection of individual pictures, showing constructions of selected triangle centers. The selections are in two groups: Recent Triangle Centers and Classical Triangle Centers.


Recent Triangle Centers

Schiffler Point
Exeter Point
Parry Point
Congruent Isoscelizers Point
Yff Center of Congruence
Isoperimetric Point and Equal Detour Point
Ajima-Malfatti Points
Apollonius Point
Morley Centers
Hofstadter Points
Equal Parallelians Point
Bailey Point
Gossard Perspector

Classical Triangle Centers

Centroid
Incenter
Circumcenter
Orthocenter
Fermat Point
Nine-point center
Symmedian point
Gergonne point
Nagel point
Mittenpunkt
Spieker center
Feuerbach point
Isodynamic points
Napoleon points
Steiner point


In addition to triangle centers, there are many interesting central lines, too. The most famous is the Euler line.


Encyclopedia of Triangle Centers - ETC
Biographical Sketches of Triangle Geometers
A Book about Triangle Centers and Central Triangles: TCCT
Clark Kimberling Home Page